In the 18-minute video, the group also objects to the name Boko Haram, Radio France Internationale reported. Its full name is Jama'atu Ahlis Sunna Lidda'awati Wal-Jihadl or People Committed to the Propagation of the Prophet's Teachings and Jihad.
"Nigerians, our name is not Boko Haram, we are Muslims, Ahlis sunnah," lyrics to the video's background music say.
Those identified as potential targets are the Hausa services of Voice of America and Radio France, the Nigerian newspaper Daily Trust and Guardian Newspapers, which owns the British papers The Guardian and Observer.
The video says it was produced by the organization's Public Awareness Department to explain why it launched a suicide attack last week in Abuja on another Nigerian newspaper, This Day: "We attacked This Day because we will never forget or forgive anyone who abused our prophet."
The footage includes clips of the This Day attack, of rifle-wielding men at prayer and of Muhammad Yusuf, the group's now-dead leader, preaching.
Boko Haram means "western education is forbidden" in Hausa. The group was founded in 2002 but only became involved in armed violence in 2009.